A running man has half the KE that a body of half his mass has. The man speeds up by `1.0ms^(-1)` and then has the same energy as the boy. What were the original speeds of the man and the boy?

Options

A. `sqrt(2) + 1`
B. `sqrt(2) -1`
C. `sqrt(2) +2`
D. `sqrt(2) -2`

Answer

A

Explanation

`K.E` of man `= (1)/(2)(K.E "of boy")`
`(1)/(2) mv^(2) = (1)/(2) ((1)/(2) (m)/(2) v_(1)^(2))`----(1)
Also given, `(1)/(2) m(v +1)^(2) = (1)/(2) (m)/(2) v_(1)^(2)` ----(2)
Divide (1) with (2) to get `v`.